Question

Three vertices of a parallelogram $ABCD$ taken in order are $A(3,6),B(5,10)$ and $C(3,2)$ find the equation of diagonal $BD$.

Answer 1

Given three coordinates of parallelogram-

$A(3,6)$

$B(5,10)$

$C(3,2)$

Now,

Mid-point of $AC$ will be equal to mid-point of $BD$.

Therefore,

Mid-point of $AC=(\frac{3+3}{2},\frac{6+2}{2})=(3,4)=$ Mid-point of $BD$

Therefore,

Equation of $BD$ will be-

$(y-10)=\frac{4-10}{3-5}(x-5)$

$(y-10)=3(x-5)$

$\Rightarrow 3x-y=5$

Hence equation of $BD$ will be-

$3x-y=5$